Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const long long inf = 1e11;
const long long mod = 1e9 + 7;
const long long N = 110;
long long a[N][N], mn = inf, n, m;
vector<long long> r(N, inf), c(N, inf);
int main() {
  ios_base::sync_with_stdio(false);
  cin >> n >> m;
  for (long long i = 0; i < (n); ++i)
    for (long long j = 0; j < (m); ++j) cin >> a[i][j];
  if (m > n) {
    for (long long i = 0; i < (n); ++i)
      for (long long j = 0; j < (m); ++j) r[i] = min(a[i][j], r[i]);
    for (long long i = 0; i < (n); ++i)
      for (long long j = 0; j < (m); ++j) c[j] = min(c[j], a[i][j] - r[i]);
  } else {
    for (long long i = 0; i < (n); ++i)
      for (long long j = 0; j < (m); ++j) c[j] = min(c[j], a[i][j]);
    for (long long i = 0; i < (n); ++i)
      for (long long j = 0; j < (m); ++j) r[i] = min(a[i][j] - c[j], r[i]);
  }
  long long br = 0;
  for (long long i = 0; i < (n); ++i)
    for (long long j = 0; j < (m); ++j)
      if (a[i][j] != r[i] + c[j]) br = 1;
  if (br == 1) {
    cout << -1;
    return 0;
  }
  long long sum = 0;
  for (long long i = 0; i < (n); ++i) sum += r[i];
  for (long long j = 0; j < (m); ++j) sum += c[j];
  cout << sum << endl;
  for (long long i = 0; i < (n); ++i)
    while (r[i]--) cout << "row " << i + 1 << endl;
  for (long long j = 0; j < (m); ++j)
    while (c[j]--) cout << "col " << j + 1 << endl;
}